First thing that would happen would be every Tom, Dick and Harry coming after you and your stuff. NO THANKS.
You would be like Salmon to a bear and no amount of firepower would be able to hold. Sheer numbers would overwhelm.
This is assuming things will have escalated to the hopeless scenario being depicted.
Think WW2 and the German invasion of Stanlingrad. It's much easier to overtake ranches/farms than cities. Many people in city are also armed. There is a Walmart every few city blockS and countless other stores. Plus surrounding our cities are countless suburbs surrounding to default to which are balance between rural and urban.
We have more places to hide were fewer would look.
High rises themselves could also become fortresses of the sky with countless barriers to no additional cost of my own.
Many people I know buy things in bulk and have at a months worth of food and water and these aren't peppers. A lot of these people will be abandoning there resources out of fear.
Within first couple days millions will have left there homes.
I'd rather go up or down than rush to middle of nowhere where I'd be sitting duck. Things never go how u think they will. Every chooch is thinking they need to leave city.
No thanks.
In my opinion staying in a large city is a death trap. You will run out of logistics very quickly. Yes a very large amount of people will flee the city in search of aid. Depending on your location in America and what time of year it is, most refugees will flee South.
Depending on the extent of the event you better have the mentality that every Tom, Dick and Harry is coming after your stuff. If you do not have situational awareness you are kind of screwing yourself(to death), it does not matter if you are rural or urban. Do not just jump to conclusion that sheer numbers will overwhelm. You have to look at.
Location: how far from the city, mode of transportation, how many days of travel to your location,
Terrain: Is your location mountainous, prairie, oceanfront, is their obstacles refugees must cross or detour.
Assets: What does your area have that would make refugees head to your location?
Attrition: You have to consider and guess what kind of resistance will the refugees meet between the city and your location. A lot of people are not going to stand by and get raped of their supplies or their neighbors. Something else to consider is that there is a way higher percentage of rural gun owners vs urban gun owners. Most liberals are pro gun control and cities tend to lean towards liberalism.
Your right cities are harder to attack and that is the reason why through history many armies will surround the cities and starve them out or catapult disease ridden bodies into the city. In a SHTF event why would someone want to go into a city. The Walmart's you mentioned will be looted out.
Something else to consider once the power is out, you loose water pressure and loose sewage removal. Gravity will win, sewage will collect down hill and work its way backwards. If you do not have a one way valve your bathroom is going to throw up raw sewage making your living area inhabitable.
High rises may become hard to attack up if you have good defenders but personally if I wanted the building I would simply smoke them out. Smoke rises and if that did not work then I would write off the building and burn them out. Heat and fire rise up. Basically if I cant have the building then nobody can and if it came to that then I probably would not take any prisoners.
Sorry to be a downer, I am looking at it from a military perspective and just do not see a long term survivability in a city.